Vehicle rollover detection system

ABSTRACT

A roll angular velocity sensor and a lateral velocity sensor are operatively coupled to a processor, which generates a signal for controlling a safety restraint system responsive to measures of roll angular velocity and lateral velocity. In one embodiment, the processor delays or inhibits the deployment of the safety restraint system responsive to a measure responsive to the measure of lateral velocity, either alone or in combination with a measure of longitudinal velocity. In another embodiment, a deployment threshold is responsive to the measure of lateral velocity. The lateral velocity may be measured by a lateral velocity sensor, or estimated responsive to measures of lateral acceleration, vehicle turn radius, and either longitudinal velocity or yaw angular velocity, wherein the turn radius is estimated from either a measure of steering angle, a measure of front tire angle, or measures of forward velocity from separate front wheel speed sensors.

[0001] The instant application claims the benefit of U.S. ProvisionalApplication Serial No. 60/366,148 filed on Mar. 19, 2002, which isincorporated herein by reference.

[0002] In the accompanying drawings:

[0003]FIG. 1a illustrates a rear view of a vehicle prior to theinitiation of a roll event;

[0004]FIG. 1b illustrates a rear view of a vehicle during a roll event;

[0005]FIG. 2 illustrates a block diagram of a rollover detection system;

[0006]FIG. 3 illustrates a flow diagram of a rollover detectionalgorithm;

[0007]FIG. 4 illustrates a flow diagram of a data acquisition andpreprocessing algorithm incorporated in the rollover detectionalgorithm;

[0008]FIG. 5 illustrates a flow diagram of a safing algorithmincorporated in the rollover detection algorithm;

[0009]FIG. 6 illustrates a flow diagram of the rollover detectionalgorithm;

[0010]FIG. 7 illustrates a flow diagram of an algorithm incorporated inthe rollover detection algorithm for determining if sensor recalibrationis required;

[0011]FIGS. 8a, 8 b and 8 c are tables that illustrate details of therollover detection algorithm;

[0012]FIGS. 9a and 9 b are tables that illustrate examples of values ofparameters of the rollover detection algorithm;

[0013]FIG. 10 illustrates a table of conditions associated with variousrollover events and non-rollover events;

[0014]FIG. 11a illustrates a plot of filtered roll rate, roll angle andfiltered lateral acceleration of a vehicle subjected to a corkscrew rolltest designated as Test A, resulting in a rollover event;

[0015]FIG. 11b illustrates a plot of filtered roll rate, roll angle andfiltered lateral acceleration of a vehicle subjected to a corkscrew rolltest designated as Test B, resulting in a non-rollover event;

[0016]FIG. 11c illustrates a plot of filtered roll rate, roll angle andfiltered lateral acceleration of a vehicle subjected to a decelerationsled test designated as Test C, resulting in a non-rollover event;

[0017]FIG. 11d illustrates a plot of filtered roll rate, roll angle andfiltered lateral acceleration of a vehicle subjected to a decelerationsled test designated as Test D, resulting in a rollover event;

[0018]FIG. 12 illustrates plots of a figure-of-merit and an associateddeployment threshold for a rollover measure as a function of time, inaccordance with a measures algorithm, for the rollover event of Test Dand the non-rollover event of Test C;

[0019]FIG. 13 illustrates a plot of roll rate as a function of time fora signal having a roll rate offset;

[0020]FIG. 14 illustrates plots of roll angle as a function of timebased upon the data of FIG. 13, for various associated processes fordetermining roll angle from roll rate;

[0021]FIG. 15 illustrates plots of roll rate as a function of rollangle, and plots of associated rollover thresholds, in accordance withan energy algorithm, for the rollover event of Test A and thenon-rollover event of Test B;

[0022]FIG. 16 illustrates an embodiment of a rollover detection systemcomprising a lateral velocity sensor;

[0023]FIG. 17 illustrates an adjustment of a roll rate—roll angledeployment threshold responsive to a measure of lateral velocity; and

[0024]FIG. 18 illustrates a threshold multiplier as a function oflateral velocity.

[0025] There exists a need for a vehicle rollover detection system thatprovides for discrimination of vehicle rollover sufficiently quickly toenable associated safety restraint actuators, e.g. seat beltpretensioners, air bags or roll curtains, to be deployed before aninitial head contact with the interior of the vehicle, particularly forthe types of rollovers resulting in relatively fast head closure times.For example, there are some roll events for which head closure may occurbefore it can be reliably determined from the physics of the roll eventwhether the vehicle will completely rollover. There further exists aneed for a robust vehicle rollover detection system that provides forsufficiently fast discrimination of vehicle rollover responsive toeither relatively slow or relatively fast rollover events.

[0026] Referring to FIG. 1a, a rollover detection system 10 is seenmounted in a vehicle 12. The vehicle 12 is shown with a local Cartesiancoordinate system with the X-axis aligned with the vehicle'slongitudinal axis—positive forward,—the Y-axis aligned with thevehicle's lateral axis—positive leftward,—and the Z-axis aligned withthe vehicle's vertical axis—positive upward. The vehicle 12 has a massM, and the associated center-of-gravity CG thereof is located at aheight Z₀ above the ground. The vehicle 12 is shown sliding at avelocity U in the negative Y direction towards an obstruction 14.

[0027] Referring to FIG. 1b, upon one or more wheels 16 of the vehicle12 engaging the obstruction 14, the resulting reaction force F therefromcauses the vehicle 12 to rotate about the X-axis relative to a trippoint 13, at a time dependent angular velocity ω_(x)(t) causing a timedependent angular position θ(t), wherein the vehicle 12 has amoment-of-inertia I_(x) about the associated axis of rotation that isparallel with the X-axis and intersecting the trip point 13. Therotation of the vehicle 12 increases the height Z_(CG) of thecenter-of-gravity CG relative to the height Z₀ thereof prior toengagement with the obstruction 14, thereby increasing the potentialenergy M·g·(Z_(CG)−Z₀) of the vehicle 12 relative to the pre-engagementposition and orientation. Accordingly, the potential energy of thevehicle 12 is dependent upon the angular position θ thereof.Furthermore, with rotation, the vehicle 12 gains an angular kineticenergy of $I_{x} \cdot {\frac{\omega_{x}^{2}}{2}.}$

[0028] . The reaction force F also causes a linear acceleration$A = \frac{F}{M}$

[0029] of the center-of-gravity CG, as indicated by the lateralacceleration component A_(y)(t) along the local Y-axis. Whereas FIGS. 1aand 1 b illustrate a roll event caused by the impact of a slidingvehicle with an obstruction, it should be understood that roll eventscan be caused by other scenarios, e.g. a tire blowout followed by asubsequent engagement of the associated wheel rim with the ground.Accordingly, the rollover detection system 10 is not limited to aparticular type of roll event.

[0030] Referring to FIG. 2, the rollover detection system 10 comprises alateral accelerometer 18 and an angular rate sensor 20, which arepreferably, but not necessarily, mounted proximate to thecenter-of-gravity CG of the vehicle 12. The lateral accelerometer 18 isresponsive to a time dependent lateral acceleration component A_(y)(t)of acceleration along the local Y-axis. For example, the lateralaccelerometer 18 may comprise an accelerometer, e.g. a micro-machinedaccelerometer having at least one axis of sensitivity, with an axis ofsensitivity substantially aligned with the local Y-axis. The angularrate sensor 20, e.g. a gyroscope, is oriented so as to be responsive toa time-dependent component of angular velocity ω_(x)(t) about the localX-axis. The lateral accelerometer 18 and angular rate sensor 20 areoperatively coupled to respective filters 22, 24 that filter therespective signals A_(y)(t) and ω_(x)(t) for processing by a processor26 having a memory 28. It should be understood that the filters 22, 24can be either separate from or incorporated in the processor 26, and maybe either analog or digital, or a combination thereof, as known to oneof ordinary skill in the art. Moreover, the filters 22, 24 could beadapted as part of the respective lateral accelerometer 18 or angularrate sensor 20. The processor 26 processes the respective filteredÃ_(y)(t) and {tilde over (ω)}_(x)(t) signals so as to discriminatewhether or not the vehicle would be likely to roll over, and responsivethereto, to control the actuation of appropriate safety restraintactuators 30 so as to mitigate rollover induced injury to an occupant ofthe vehicle 12. For example, the processor 26 may comprise a digitalcomputer, microprocessor or other programmable device, an analogprocessor, analog or a digital circuitry, or a combination thereof.Moreover, the safety restraint actuators 30 may include, but are notlimited to, a seat belt pretensioner 32 operatively connected to a seatbelt 34; a thorax air bag inflator 36 adapted to provide protection fromboth rollover and side-impact crashes; a roll curtain 38 adapted todeploy between the occupant and the side window 39 of the vehicle 12; oran overhead air bag inflator 40 adapted to deploy an air bag from theroof or headliner of the vehicle 12. Whereas FIG. 2 illustrates thesafety restraint actuators 30 for one seating position of the vehicle12, it should be understood that safety restraint actuators 30 may beprovided at each seating position, and that the rollover detectionsystem 10 can be adapted to control any or all of the safety restraintactuators 30 responsive to rollovers in any direction for which theassociated safety restraint actuators 30 are adapted to mitigateoccupant injury. Moreover, the particular set of safety restraintactuators 30 need not necessarily include all of those describedhereinabove, or may include other types of safety restraint actuators 30not described hereinabove.

[0031] Referring to FIG. 3, in accordance with one embodiment of arollover detection algorithm 100 for detecting a vehicle rollover andcontrolling the actuation of one or more associated safety restraintactuators 30—e.g. in accordance with the apparatus illustrated in FIG.2—comprises the combination of a data acquisition and preprocessingalgorithm 150, a measures algorithm 300.1, an energy algorithm 300.2, asafing algorithm 200 and associated logic 330′, 340 that generates asignal 342 that controls the actuation of the safety restraintactuator(s) 30 responsive thereto.

[0032] The measures algorithm 300.1 uses a heuristic, time-domaindiscrimination process to detect a rollover condition, and can bebeneficial in shortening deployment times for most rollover eventscharacterized by relatively fast head closure times (e.g. <250 msec)that are typically associated with larger lateral vehicle forces. Themeasures algorithm 300.1 utilizes both the filtered lateral accelerationcomponent Ã_(y) and filtered angular velocity {tilde over (ω)}_(x)signals to evaluate a function that is compared with a threshold, thatalong with other criteria, are used to make a deployment decision.

[0033] The energy algorithm 300.2 uses a phase-space discriminationprocess—based upon the physics associated with a vehicle rolloverprocess—to detect a rollover condition, and can be beneficial inproviding reliable deployment decisions for slower roll events that arecaused primarily by vertical forces on the vehicle or by low levellateral forces on the vehicle 12. The energy algorithm 300.2 utilizesthe filtered angular velocity {tilde over (ω)}_(x) signal to determinethe roll state of the vehicle 12 and to compare the instantaneous totalenergy (rotational to kinetic and potential) thereof with that needed tocause the vehicle 12 to roll past an associated equilibrium position.The energy algorithm 300.2 utilizes both the filtered lateralacceleration component Ã_(y) and filtered angular velocity {tilde over(ω)}_(x) signals in the associated entrance and exit criteria.

[0034] Whereas FIG. 3 illustrates the measures algorithm 300.1 and theenergy algorithm 300.2 used in combination, it should be understood thatthis is not essential, and that either of the algorithms can be usedalone. However, the combination of algorithms increases the robustnessof the associated rollover detection system 10, because for someconditions, e.g. “curb-trip” conditions, the measures algorithm 300.1can provide faster discrimination than the energy algorithm 300.2;whereas for other conditions, e.g. “corkscrew”, “ramp” or “flip”conditions, the energy algorithm 300.2 can provide faster discriminationthan the measures algorithm 300.1.

[0035] The measures algorithm 300.1 and energy algorithm 300.2 areindependent of one another, although each utilizes common, filtered datafrom the data acquisition and preprocessing algorithm 150, i.e. afiltered lateral acceleration components Ã_(y) and a filtered angularvelocity {tilde over (ω)}_(x). Both the measures algorithm 300.1 and theenergy algorithm 300.2 are characterized by associated entrance and exitcriteria, wherein calculations associated with the respective algorithmare commenced if the respective associated entrance criteria issatisfied, and these calculations are terminated if the respectiveassociated exit criteria is satisfied, and then reset if and when theentrance criteria are subsequently satisfied.

[0036] The safing algorithm 200 can improve the reliability of therollover detection system 10 by providing an independent set ofconditions, or safing criteria—dependent upon the filtered lateralacceleration components Ã_(y) and/or filtered angular velocity {tildeover (ω)}_(x)—that must be met in order to enable the deployment of theone or more associated safety restraint actuators 30. Both the measuresalgorithm 300.1 and the energy algorithm 300.2 are each “csafed” by acommon safing algorithm 200. Whereas the safing algorithm 200 providesfor additional discrimination so as to mitigate against an undesirableactuation of the safety restraint actuators 30 responsive tonon-rollover events, it should be understood that the safing algorithm200 is not essential, and that either measures algorithm 300.1 or theenergy algorithm 300.2 can be used alone, or in combination with oneanother, with or without the safing algorithm 200.

[0037] In the operation of the rollover detection algorithm 100,responsive to data from the data acquisition and preprocessing algorithm150, if either the measures algorithm 300.1 OR 330′ the energy algorithm300.2 detects a vehicle rollover condition, AND 340 if the safingalgorithm 200 determines that an associated independent safing conditionis satisfied, then, in step (350), one or more safety restraintactuators 30 are deployed so as to mitigate injury to an associatedoccupant of the vehicle, that could result from the rollover event,whether or not the vehicle 12 actually rolls over.

[0038] The data acquisition and preprocessing algorithm 150, safingalgorithm 200, measures algorithm 300.1, and energy algorithm 300.2 aredescribed hereinbelow with reference to flow charts illustrated in FIGS.3-7. FIG. 6 illustrates a flow chart of a general algorithmic structureof both the measures algorithm 300.1 and the energy algorithm 300.2,wherein particular details of the measures algorithm 300.1 and theenergy algorithm 300.2 are provided in table format in FIGS. 8a-c. Thealgorithms are described mathematically, wherein parameters are used forapplication specific constants, and these parameters are listed in FIGS.9a and 9 b along with exemplary values for a particular type of vehicle.It should be understood that the parameters are generally adapted to aparticular application, e.g. vehicle platform, and that the particularvalues of the parameters in FIGS. 9a and 9 b are illustrative only, andshould not be considered to limit the scope of the instant invention.

[0039] Referring to FIG. 4, the data acquisition and preprocessingalgorithm 150 acquires a measurement of lateral acceleration componentA_(y) from the lateral accelerometer 18 in step (152), and acquires ameasurement of longitudinal angular velocity ω_(x), or roll rate, fromthe angular rate sensor 20 in step (158). Data from more than 100rollover tests has indicated that the angular velocity ω_(x) associatedwith a rollover generally ranges between ±300 degrees/second(±|ω_(x)^(max)|)

[0040] and the lateral acceleration component A_(y)(t) associatedtherewith generally ranges between ±20  g  (±|A_(Y)^(max)|)

[0041] Respective measurements of the lateral acceleration componentA_(y)(t) and the angular velocity ω_(x) that exceed these respectivelimits are respectively clipped thereat in steps (154) and (160)respectively. For example, the value of an lateral accelerationcomponent A_(y)(t) measurement less that −20 g would be set in step(154) to −20 g, for the example of an associated range of ±20 g. Thepolarities of the lateral accelerometer 18 and the angular rate sensor20 are set so that the corresponding polarities of angular velocityω_(x) and the lateral acceleration component A_(y) signals are the sameas each other during a roll event. Generally, the level |A_(Y)^(max)|

[0042] for clipping signals from the lateral accelerometer 18 is set tothe minimum of either 20 g or the range of the lateral accelerometer 18.Similarly, the level |ω_(x)^(max)|

[0043] for clipping signals from the angular rate sensor 20 is set tothe minimum of either 300 degrees/second or the range of the angularrate sensor 20.

[0044] The raw lateral acceleration component A_(y) and angular velocityω_(x) data from the lateral accelerometer 18 and the angular rate sensor20 respectively are filtered by respective filters 22, 24 in steps (156)and (162) respectively, so as to respectively provide a filtered lateralacceleration component Ã_(y) and a filtered angular velocity {tilde over(ω)}_(x). The use of filtered measurements is beneficial in avoiding afalse entrance of the roll discrimination algorithm, and in improvingthe associated discrimination process by the measures algorithm 300.1and the energy algorithm 300.2. The filters 22, 24 are, for example,moving average filters having a moving average window of T_(Avg), e.g.between 10 and 15 milliseconds, so as to provide a suitable compromisebetween fast signal response and noise reduction. As an example, for aprocessor 26 that uniformly samples the angular velocity ω_(x) andlateral acceleration component A_(y) signals—as is assumedhereinbelow—with a sampling rate of 2500 Hz (corresponding to a sampleperiod dt=0.4 milliseconds) and a window of 12.8 milliseconds, a movingaverage for each signal would be calculated from the last 32 samplesacquired. The individual samples of the moving average are typicallyuniformly weighted, but could alternately be non-uniformly weighted.

[0045] Generally, the lateral accelerometer 18 and the angular ratesensor 20 can exhibit offset and/or drift error (generally referred toherein as sensor offset error), which, unless otherwise compensated, cancause associated roll detection errors. The sensor offset errors areestimated by filtering the associated sensor measurements withassociated filters having an effective cutoff frequency that issubstantially lower—or, stated in another way, a effective filter timeconstant that is substantially greater—than the associatedabove-described moving-average filters that provide the filtered lateralacceleration component Ã_(y) and the filtered angular velocity {tildeover (ω)}_(x). For example, the acceleration offset${\overset{\sim}{A}}_{y}^{Offset}$

[0046] and the angular velocity offset${\overset{\sim}{\omega}}_{x}^{Offset}$

[0047] are filtered from the associated raw measurements of angularvelocity ω_(x) and lateral acceleration component A_(y) respectively, byrespective moving average filters in steps (168) and (170) respectively,each moving-average filter having an associated filter window of widthT_(Avg) _(—) _(Offset), e.g. about 4 seconds. From step (164), thefiltered values of acceleration offset${\overset{\sim}{A}}_{y}^{Offset}$

[0048] and angular velocity offset${\overset{\sim}{\omega}}_{x}^{Offset}$

[0049] are updated only if the neither the measures algorithm 300.1 northe energy algorithm 300.2 have been entered, as indicated by neitherassociated ONGOING_EVENT_FLAGs—i.e. neither anONGOING_MEASURES_EVENT_FLAG nor an ONGOING_ENERGY_EVENT_FLAG—being set.Accordingly, in step (166), the relatively long-term filtered values ofacceleration offset ${\overset{\sim}{A}}_{y}^{Offset}$

[0050] and angular velocity offset${\overset{\sim}{\omega}}_{x}^{Offset}$

[0051] are not updated during periods of time when the associatedlateral acceleration component A_(y) and angular velocity ω_(x) could besubstantially different from the associated sensor offset values.

[0052] Whereas FIG. 4 illustrates the acquisition and processing of thelateral acceleration component A_(y) before that of the angular velocityω_(x), it should be understood that the relative order could bereversed, or these operations could be performed in parallel.

[0053] The measures algorithm 300.1, energy algorithm 300.2, and thesafing algorithm 200 each utilize values of filtered lateralacceleration component Ã_(y) and filtered angular velocity {tilde over(ω)}_(x) that are compensated by subtracting the corresponding sensoroffsets, i.e. the acceleration offset ${\overset{\sim}{A}}_{y}^{Offset}$

[0054] and the angular velocity offset${\overset{\sim}{\omega}}_{x}^{Offset}$

[0055] respectively, so as to provide a corresponding compensatedlateral acceleration component$\left( {{A_{y}^{\prime}(t)} = {{{\overset{\sim}{A}}_{y}(t)} - {{\overset{\sim}{A}}_{y}^{Offset}(t)}}} \right)$

[0056] and a compensated angular velocity$\left( {{\omega_{x}^{\prime}(t)} = {{{\overset{\sim}{\omega}}_{x}(t)} - {{\overset{\sim}{\omega}}_{x}^{Offset}(t)}}} \right)$

[0057] respectively.

[0058] Referring to FIG. 5, the safing algorithm 200 commences with step(202), wherein associated SAFING_EVENT_FLAGs i.e. anACCELERATION_SAFING_EVENT_FLAG and a ROLL_SAFING_EVENT_FLAG—areinitially reset. Then, in step (204), if either the measures algorithm300.1 or the energy algorithm 300.2 have been entered, as indicated byeither of the associated ONGOING_EVENT_FLAGs (i.e. theONGOING_MEASURES_EVENT_FLAG or the ONGOINGENERGY_EVENT_FLAG) being set,then in step (206), if the magnitude of the compensated lateralacceleration component A′_(y) is greater than a third accelerationthreshold A_(y)^(Thr_3),

[0059] , then the ACCELERATION_SAFING_EVENT_FLAG is set in step (208).Otherwise, from step (204), the process repeats with step (202).Following step (208), or otherwise from step (206), in step (210), ifthe magnitude of the compensated angular velocity ω′_(x) is greater thana third angular velocity threshold ω_(x)^(Thr_3),

[0060] , then the ROLLSAFING_EVENT_FLAG is set in step (212). Then, orotherwise from step (210), the process repeats with step (204).Accordingly, if the conditions on lateral acceleration and angularvelocity associated with the safing algorithm 200 have beensatisfied—not necessarily simultaneously—after at least one of themeasures algorithm 300.1 and the energy algorithm 300.2 have commencedand before both have exited, then the respective associatedSAFING_EVENT_FLAGs are set so as to enable a deployment of the one ormore associated safety restraint actuators 30 responsive to thedetection of a roll event by either the measures algorithm 300.1 or theenergy algorithm 300.2. Each of the SAFING_EVENT_FLAGs are set, orlatched, separately, but both are reset simultaneously, and both must beset in order for the one or more associated safety restraint actuators30 to be actuated responsive to the measures algorithm 300.1 or theenergy algorithm 300.2.

[0061] Alternately, the safing algorithm 200 may be adapted toincorporate only one of the above-described SAFING_EVENT_FLAGs andassociated criteria, so that the safing criteria is responsive to atleast one of a magnitude of the compensated lateral accelerationcomponent A′_(y) being greater than a third acceleration thresholdA_(y)^(Thr_3)

[0062] at a first point of time following a time of inception of eitherthe measures algorithm 300.1 or the energy algorithm 300.2, and amagnitude of the compensated angular velocity ω′_(x) being greater thana third angular velocity threshold ω_(x)^(Thr_3)

[0063] at a second point of time following the time of inception,wherein the time of inception is the time at which the associatedentrance criteria are satisfied for the associated measures algorithm300.1 or energy algorithm 300.2, and the first and second points of timefollowing the time of inception are arbitrary with respect to oneanother. For example, the energy algorithm 300.2 could be “safed”responsive solely to the compensated lateral acceleration componentA′_(y) being greater than a third acceleration threshold A_(y)^(Thr_3)

[0064] at a point of time following a time of inception of the energyalgorithm 300.2.

[0065] The rollover detection system 10 may be adapted for improvedreliability by implementing the safing algorithm 200 on a microprocessorthat is separate from that used to implement either the measuresalgorithm 300.1 or the energy algorithm 300.2, in which case if thesating algorithm 200 is not aware of the ONGOING_EVENT_FLAGs, theninstead of being reset responsive to these flags, the SAFING_EVENT_FLAGsmay be reset after a delay, e.g. Δ  t_(max)^(E)

[0066] (e.g. 12 seconds), following a point in time at which eithersafing criteria was last satisfied so that the safing condition remainsactive until either a deployment of the one or more associated safetyrestraint actuators 30, or until after both algorithms will have had tohave exited.

[0067] The measures algorithm 300.1 and the energy algorithm 300.2 eachoperate in accordance with the general algorithmic structure illustratedin FIG. 6, wherein each of these algorithms is indicated generally byreference number 300. A decimal designator to a particular referencenumber will be used herein to refer to a particular algorithm. Forexample, whereas the general overall process is referred to by referencenumber 300, reference number 300.1 is used to refer to the measuresalgorithm, and reference number 300.2 is used to refer to the energyalgorithm. As an other example, whereas the general algorithmcalculations step is referred to by reference number 326, referencenumber 326.1 is used to refer to the algorithm calculations step of themeasures algorithm 300.1 in particular, and reference number 326.2 isused to refer to the algorithm calculations step of the energy algorithm300.2. The particular equations associated with particular algorithmicsteps, for each of the algorithms, are provided in tabular form in FIGS.8a-c; and the associated parameters and exemplary values thereof areprovided in tabular form in FIGS. 9a-b.

[0068] Referring to FIG. 6, the general roll processing algorithmcommences with step (302), wherein a corresponding ONGOING_EVENT_FLAG isreset. The ONGOING_EVENT_FLAG, when set, indicates that the entrancecriteria has been satisfied for the roll processing algorithm, and thecorresponding exit criteria has not been satisfied, so that theassociated algorithm is active. Then in step (150), the associated datathat is used by the algorithm is acquired and preprocessed in accordancewith the data acquisition and preprocessing algorithm 150 describedhereinabove. Then, in step (304), if the ONGOING_EVENT_FLAG has not beenset—indicating that data from a potential roll event is not beingprocessed, and that the vehicle 12 is not then involved in a rollevent—then, in step (306), a set of entrance criteria are evaluated andcompared with associated thresholds, and if the entrance criteria aresatisfied, then in step (308) the ONGOING_EVENT_FLAG is set, and in step(310), the algorithm is initialized, e.g. by initializing variousdynamic variables associated with the algorithm.

[0069] Otherwise, from step (304), if the ONGOING_EVENT_FLAG has beenset—indicating that data from a potential roll event is beingprocessed,—then in step (312) an associated measure of time, e.g. samplecount, is updated, and in step (400), the newly acquired data isevaluated so as to determine if a sensor (i.e. the lateral accelerometer18 or the angular rate sensor 20) needs to be recalibrated. The processassociated with step (400) is illustrated in FIG. 7 and is describedmore fully hereinbelow.

[0070] If, from step (400), one or more sensors require recalibration,then in step (314), the one or more sensors requiring recalibation arerecalibrated. For example, both the lateral accelerometer 18 and theangular rate sensor 20 may be testable, wherein a known stimulus may beapplied to the sensor, and the corresponding sensor output may becalibrated so as to represent the known stimulus. For example, thelateral accelerometer 18 may comprise a micro-machined mass elementsuspended by spring-element beams, and an electrostatic field may beapplied between the mass element and a housing so as to deflect the beamby an amount that corresponds to a reference acceleration level. Acalibration factor is then calculated so that the calibrated output fromstrain sensing elements operatively connected to the spring-elementbeams corresponds to the reference acceleration level. If, in step(316), the process of step (314) indicates that one or more sensors havefailed—for example, if there is substantially no change in outputresponsive to whether or not the test stimulus is applied to the sensor,then in step (318) a fault condition is set; a warning device, e.g.light, is activated so as to alert the driver of the vehicle 12; and therollover detection system 10 is disabled from deploying any safetyrestraint actuators 30. Otherwise, from step (316), i.e. if neither thelateral accelerometer 18 nor the angular rate sensor 20 has failed,then, in step (320), both ONGOING_EVENT_FLAGs—i.e. theONGOING_MEASURES_EVENT_FLAG and the ONGOING_ENERGY_EVENT_FLAG—are resetresponsive to there having been at least one sensor recalibration, andthe process repeats anew with step (150).

[0071] Otherwise, from step (400), if none of the sensors requirerecalibration, then, in step (322), an exit criteria is evaluated so asto determine whether the algorithm should be exited until such time thatthe entrance criteria of step (306) are again satisfied so as to enablethe algorithm to be reentered. If, from step (322), the exit criteriaare satisfied, then, in step (324), if the algorithm is the energyalgorithm 300.2, and if the energy algorithm 300.2 has consecutivelybeen entered in step (306), and then exited in step (322) as a result ofa time-out (i.e.Δ  t > Δ  t_(max)^(E)),

[0072] , then reentered in step (306) shortly—e.g. during the nextiteration of the algorithm—after exiting in step (322), then after thep^(th) consecutive exit in step (322)—e.g. p=3—the process continueswith step (314) as described hereinabove, wherein the sensors arediagnosed, and if necessary, recalibrated. Otherwise, from step (324),the associated ONGOING_EVENT_FLAG—i.e. the ONGOING_MEASURES_EVENT_FLAGor the ONGOING_ENERGY_EVENT_FLAG—is reset in step (320), and the processrepeats anew with step (150).

[0073] Otherwise, from step (322), if the algorithm has been entered instep (306) and not exited in step (322), then the associated algorithmcalculations are performed for the particular iteration of the algorithmassociated with a particular value of the measure of time from eithersteps (310) or (312). Then, in step (330), if the associated algorithmdetection criteria are satisfied in the particular iteration of thealgorithm, and if, in step (340), the SAFING_EVENT_FLAG(s)—i.e. theACCELERATION_SAFING_EVENT_FLAG and the ROLL_SAFING_EVENT_FLAG—have beenset, then in step (350) a roll event has been detected, and theassociated safety restraint actuators 30 are actuated. Otherwise either,from step (330), if the algorithm detection criteria are not satisfied,or, from step (340), if all of the SAFING_EVENT_FLAG(s) have not beenset—so that the associated safing criteria has not been satisfied atsome point in time during either the measures algorithm 300.1 or theenergy algorithm 300.2, then the process continues repeats beginningwith step (150) for the next iteration.

[0074] Although both the measures algorithm 300.1 and the energyalgorithm 300.2 depend upon measurements of the lateral accelerationcomponent A_(y) and the longitudinal angular velocity ω_(x) from thedata acquisition and preprocessing algorithm 150, the other variablesand parameters associated with each algorithm are otherwise independentof one another, as are the associated entrance criteria in step (306),algorithm initializations in step (310), exit criteria in step (322),algorithm calculations in step (326), and algorithm decision criteria instep (330), examples of all of which are detailed in FIGS. 8a, 8 b, 8 c,9 a and 9 b. For example, whereas each algorithm determines a measure oftime since inception, and calculates a measure of roll angle byintegrating the measurement of longitudinal angular velocity ω_(x),these respective measures of time are independent of one another, as arethe respective measures of roll angle. Both the measures algorithm 300.1and the energy algorithm 300.2 assume that the vehicle is initiallylevel (i.e. θ(t_(entrance))=0) when the processing by the respectivealgorithms is commenced.

[0075] The process 400 for determining whether or not either the lateralaccelerometer 18 or the angular rate sensor 20 requires recalibration isillustrated in FIG. 7. In steps (402), (404), (406) and (408), if themagnitude of the filtered angular velocity {tilde over (ω)}_(x)continuously exceeds a fourth angular rate threshold ω_(x)^(Thr_4)

[0076] for an associated period of time Δ  t_(ω)^(max),

[0077] , then a recalibration of the angular rate sensor 20 is signaledin step (410). Otherwise, in steps (412), (414), (416), (418) and (420),if the either the magnitude of the roll angle θ^(M) from the measuresalgorithm 300.1, or roll angle θ^(E) from the energy algorithm 300.2,continuously exceeds a roll angle threshold θ^(Thr) for an associatedperiod of time Δt_(θ) ^(max), then a recalibration of the angular ratesensor 20 is signaled in step (410). Otherwise, in step (422), arecalibration of the angular rate sensor 20 is not signaled. In steps(424), (426), (428) and (430), if the magnitude of the filtered lateralacceleration component Ã_(y) continuously exceeds a fourth lateralacceleration threshold A_(y)^(Thr_4)

[0078] for an associated period of time Δ  t_(A)^(max),

[0079] , then a recalibration of the lateral accelerometer 18 issignaled in step (432). Otherwise, in step (434), a recalibration of thelateral accelerometer 18 is not signaled. If a recalibration wassignaled in either steps (410) or (432), then the process continues withstep (314) as described hereinabove. Otherwise, no sensor recalibrationis signaled, and the process continues with step (322) as describedhereinabove.

[0080] Referring to FIG. 6, FIGS. 8a-c, and FIGS. 9a-b, the measuresalgorithm 300.1 will now be discussed with greater particularity,wherein the steps of FIG. 6 are suffixed with “0.1” to indicate theirassociation therewith. The ONGOING_EVENT_FLAG for measures algorithm300.1—referred to as the ONGOING_MEASURES_EVENT_FLAG—is set in step(308.1) upon satisfaction of the entrance criteria in step (306.1), andis reset in step (320.1) upon satisfaction of the exit criteria in step(322.1). The ONGOING_MEASURES_EVENT_FLAG, for example, could correspondto a particular location in the memory 28 of the associated processor 26that implements the measures algorithm 300.1. After entry following step(306.1), the measures algorithm 300.1 is not subsequently exited untileither the measures event exit criteria is satisfied in step (322.1), oruntil a roll event is detected causing a deployment of the safetyrestraint actuators 30. Moreover, after the measures event exit criteriais satisfied and the measures algorithm 300.1 is exited, the measuresalgorithm 300.1 can be subsequently reentered if the associated measuresevent entrance criteria is subsequently satisfied.

[0081] In step (306.1), the entrance criteria of the measures algorithm300.1 is, for example, that the magnitude of the compensated lateralacceleration component A′_(y) be greater than a first accelerationthreshold A_(y)^(Thr_1),

[0082] , i.e.: A_(y)^(′)(t) > A_(y)^(Thr_1)

[0083] For an example of one particular type of vehicle, based uponactual rollover data, the first acceleration threshold A_(y)^(Thr_1)

[0084] was set to about 1.4 g. It should be recognized that thisthreshold value, as well as the value of the other parameters of themeasures algorithm 300.1, is generally dependent upon thecharacteristics of the particular associated vehicle 12 or class ofvehicles, and that the particular value used for a particular rolloverdetection system 10 can be adjusted for improved discriminationdependent upon the nature of the associated vehicle 12 or class ofvehicles.

[0085] In step (310.1), upon initial entrance to the measures algorithm300.1 following step (308.1), the measures algorithm 300.1 isinitialized. An event sample count nm and the values of angular positionθ^(M) (n^(M)−1) and a measure function R(n^(M)−1) are initialized—e.g.to values of zero. Also the sampled time t^(M)(−1) just prior to thetime of event entrance is initialized to a value of the time of measuresevent entrance t^(M)(0), which is initialized to a value of the currenttime t; and the time period Δt^(M)(0) since algorithm entrance isinitialized to a value of zero. The superscript “M” used herein refersto variables associated with the measures algorithm 300.1.

[0086] Upon subsequent iteration of the measures algorithm 300.1, if instep (304.1) the ONGOING_MEASURES_EVENT_FLAG is set, then, in step(312.1), the event sample count n^(M) is incremented, the associatedcurrent sampled time t^(M)(n^(M)) is set equal to the current time t,and the measures event time Δt^(M) is calculated as the period extendingfrom the time of measures event entrance t^(M)(0), to the current timet^(M)(n^(M)) as follows:

Δt ^(M)(n ^(M))=t ^(M)(n ^(M))−t ^(M)(0)

[0087] In step (322.1), the exit criteria of the measures algorithm300.1 is, for example, that the time period since algorithm entranceΔt^(M) (n^(M)) be greater than time period threshold Δ  t_(max)^(M),

[0088] , i.e.: Δ  t^(M)(n^(M)) > Δ  t_(max)^(M)

[0089] For the example of one particular type of vehicle, based uponactual rollover data, the time period threshold Δ  t_(max)^(M)

[0090] was set to about 165 milliseconds. Upon exit from the measuresalgorithm 300.1, the ONGOING_MEASURES_EVENT_FLAG is reset in step(320.1), and pending subsequent satisfaction of the entrance criteria instep (306.1), this causes the variables associated with the measuresalgorithm 300.1 to be initialized in step (310.1).

[0091] If, in step (322.1), the exit criteria is not satisfied, then thealgorithm calculations are updated in step (326.1) for the particulariteration of the measures algorithm 300.1, as follows.

[0092] First, the angular position θ^(M) is estimated by integrating thesigned value of the compensated angular velocity ω′_(x) as follows:

θ^(M)(n ^(M))=θ^(M)(n ^(M)−1)+{tilde over (ω)}′_(x)(n ^(M))·dt

[0093] wherein the integration time step dt is given by the differencebetween the time t^(M)(n^(M)) at the current iteration, and the time atthe previous iteration t^(M)(n^(M)−1) which difference would be constantfor a uniform sampling rate—as follows:

dt=t ^(M)(n ^(M))−t ^(M)(n ^(M)−1)

[0094] and the compensated angular velocity ω′_(x) is given by:${\omega_{x}^{\prime}(t)} = {{{\overset{\sim}{\omega}}_{x}(t)} - {{\overset{\sim}{\omega}}_{x}^{Offset}(t)}}$

[0095] A measure function R is then evaluated, which is used tocalculate a figure-of-merit FOM. The measure function R is given by:${R\left( n^{M} \right)} = {{{R\left( {n^{M} - 1} \right)} \cdot \left( {1 - \frac{\Delta \quad t^{M}}{\tau}} \right)} + {F^{*} \cdot {KE}^{*} \cdot {PE}^{*}}}$

[0096] The first term of the measure function R is a damping termcomprising the product of the previous value, R(n^(M)−1) multiplied by adamping factor $\left( {1 - \frac{\Delta \quad t^{M}}{\tau}} \right).$

[0097] . The level of damping is determined by a constant τ dependentupon the particular type of vehicle. For example, based upon rollovertest data for a particular type of vehicle, the value of τ wasdetermined to be about 400 seconds. The damping term ensures that theresulting figure-of-merit FOM will decrease for events for which thevalues of the compensated lateral acceleration component A′_(y) or thecompensated angular velocity ω′_(x) do not continue to be significant.

[0098] The remaining term of the measure function R, additive with thefirst term, is the product of the following three measures: a forcemeasure F*, a rotational kinetic energy measure KE*, and a potentialenergy measure PE*.

[0099] The force measure F* is given as the current sample of thecompensated lateral acceleration component A′_(y), which is given by:${A_{y}^{\prime}\left( n^{M} \right)} = {{{\overset{\sim}{A}}_{y}(t)} - {{\overset{\sim}{A}}_{y}^{Offset}(t)}}$

[0100] Generally, force and acceleration are related by Newton's secondlaw (F=M·A). The force measure F* is not necessarily an exact measure offorce—which would generally need to account for the vector nature offorce and acceleration—but instead is a measure that is at least relatedto the reaction force F acting upon the vehicle 12. During a typicalvehicle roll event, the compensated lateral acceleration componentA′_(y), is caused by a lateral force on the tires or wheel rim. Thislateral force is the same force responsible for the rotational torqueabout the center of vehicle mass that leads to eventual rollover. Thecompensated lateral acceleration component A′_(y) does not necessarilyprovide a complete measure of the actual reaction force F. For example,the compensated lateral acceleration component A′_(y) does notnecessarily account for the effects of non-rigid body dynamics, e.g.from damping forces in the tire(s) or other damping elements, or fromthe dynamics of the suspension system. However, the compensated lateralacceleration component A′_(y) is heuristically—for small angles andexcluding the effects of non-rigid body dynamics—proportional to thereaction force F that causes the vehicle 12 to roll. Data from fast ortripped rollover tests has shown that the compensated lateralacceleration component A′_(y) becomes significant about 20 millisecondsbefore significant compensated angular velocity ω′_(x) is observed fromangular rate sensor 20. Whereas the force measure F* is illustratedherein as linear with respect to the compensated lateral accelerationcomponent A′_(y), it should be understood that the force measure F*could be some other function (other than linear) or power (other than 1)of the compensated lateral acceleration component A′_(y).

[0101] The rotational kinetic energy measure KE* is given by {tilde over(ω)}′_(x) ². Generally, the rotational kinetic energy measure KE* isrelated to the rotational kinetic energy of the vehicle. For example,with ${{KE}^{*} = {\overset{\sim}{\omega}}_{x}^{\prime 2}},$

[0102] , the rotational kinetic energy measure KE* is proportional tothe rotational kinetic energy of the vehicle 12 by the proportionalityconstant I_(x)/2. However, the rotational kinetic energy measure KE*could also be represented differently. For example, other powers of{tilde over (ω)}′_(x) other than 2 could be used to form the rotationalkinetic energy measure KE* from compensated angular velocity ω′_(x), orthe rotational kinetic energy measure KE* could be some other functionof compensated angular velocity ω′_(x).

[0103] The product of the force measure F* and the rotational kineticenergy measure KE* provides for a measure that predicts rollover morequickly than compensated angular velocity ω′_(x) alone. This alsoprovides a predictive measure of eventual compensated angular velocityω′_(x), because it has been observed that significant lateral forceinferred from the compensated lateral acceleration component A′_(y)usually manifests as increased compensated angular velocity ω′_(x) about20 milliseconds thereafter. Moreover, weighting the compensated angularvelocity ω′_(x) more heavily than the compensated lateral accelerationcomponent A′_(y), e.g. by using the square of the compensated angularvelocity ω′_(x), increases the influence of actual compensated angularvelocity ω′_(x) upon the resulting figure-of-merit FOM.

[0104] The potential energy measure PE* is given as PE*=sign(A′_(y)(n^(M)))·θ₀+θ^(M)(n^(M)) as a constant plus the current sample ofthe angular position θ^(M)(n^(M)). The constant θ₀ is dependent upon theparticular vehicle. For example, based upon rollover test data for aparticular type of vehicle, the value of θ₀ is about 0.1 degrees. Theconstant term has the same sign as either the compensated angularvelocity ω′_(x) or the compensated lateral acceleration componentA′_(y), assuming both signals are polarized so as to have the samepolarity for a given roll event. Including the potential energy measurePE* in the product term of the measure function R increases theinfluence of roll dynamics upon the resulting figure-of-merit FOM andincreases the magnitude thereof for medium-speed roll events, forexample, events having associated actuator firing times (time-to-fireTTF) of typically between 140 and 230 milliseconds. (The bounds of thisrange could be extended by 20% or more depending upon the vehiclecharacteristics, and could be further different for different types ofvehicles). Compared with the force measure F* and with the rotationalkinetic energy measure KE*, the potential energy measure PE* isrelatively less significant, and could be ignored (e.g., by settingPE*=1) in a reduced rollover detection system 10. However, the potentialenergy measure PE* appears to be beneficial for the subset of roll eventcases exhibiting intermediate actuator firing times.

[0105] The figure-of-merit FOM is then given by:

FOM(n ^(M))=|R(n ^(M))|·(R(n ^(M))|−|R(n ^(M)−1)|)

[0106] The figure-of-merit FOM is calculated from the absolute values ofthe associated R(n^(M)) and R(n^(M)−1) terms so that the figure-of-meritFOM is independent of the direction of roll. The term(|R(n^(M))|−|R(n^(M)−1)|) provides a measure of the derivative or slopeof the measure function R with respect to time, wherein the actual slopewould be given by dividing this term by the sampling period dt (aconstant in uniformly sampled data systems). This slope factor, incombination with a threshold function described below, has the effect ofrequiring the figure-of-merit FOM to increase with time in order for arollover event to be detected and for a resulting associated deploymentof one or more safety restraint actuators 30.

[0107] Alternately, and particularly for relatively small values of(|R(n^(M))|−|R(n^(M)−1)|), the figure-of-merit FOM may be given by:

FOM(n ^(M))=|R(n ^(M))|

[0108] Following the algorithm calculations of step (322.1), thealgorithm detection criteria evaluated in step (330.1) comprise aplurality of detection conditions, for example, as illustrated in FIG.8c. If all of the detection conditions are satisfied—so that generally ameasures event threshold is exceeded—then a rollover is consideredlikely to occur, and if in step (340), an associated safing criteria issatisfied from the safing algorithm 200, then in step (350), theassociated one or more safety restraint actuators 30 are deployed so asto mitigate injury to the associated occupant or occupants. Thedetection criteria are established in accordance with a particulardetection philosophy. Ideally, the detection criteria would IS providefor detection of any roll event for which there would be a head contactwith the interior of the vehicle (i.e. a “head closure”) of sufficientseverity that injury to the occupant therefrom would be mitigated by atimely deployment of the associated one or more safety restraintactuators 30; and would provide for ignoring other events. However, ifsuch ideal performance is not feasible, then the detection criteria canbe adapted to provide a suitable compromise. For example, in order todetect severe roll events sufficiently fast—i.e. sufficiently soonerthan the associated head closure time so that the associated one or moresafety restraint actuators 30 can be actuated in time, and at a rate, soas to mitigate risk of injury to the occupant—it may be necessary toaccept deployment of the associated one or more safety restraintactuators 30 responsive to severe rollover events that do not completelyroll the vehicle (e.g. curb trip or mid-to-high-g deceleration type rollevents).

[0109] As a first detection condition of step (330.1), the measuresevent time Δt^(M) is tested to be within a range of measures event times(Δt^(M) _(min), Δt^(M) _(max)), as follows:Δ  t_(min)^(M) ≤ Δ  t^(M) ≤ Δ  t_(max)^(M)

[0110] For example, the associated minimum and maximum event times forone particular class of vehicles are Δ  t_(min)^(M) = 40

[0111] milliseconds and Δ  t_(max)^(M) = 165

[0112] milliseconds, so that the period of time elapsed since the eventtrigger falls within a particular time window. The minimum measuresevent time Δ  t_(max)^(M)^(n)

[0113] constraint prevents hard lateral input force events of very shortduration from causing an inadvertent detection, while allowing for asufficiently early safety restraint deployment to satisfy the earliestobserved head closure times. (The head closure time is the time at whichthe head of an occupant contacts the interior of the vehicle).Typically, for severe curb trip or deceleration sled events, the rolldiscrimination algorithm entrance time would occur about 20 millisecondsafter the start of the roll event (i.e. the beginning of the physicalevent). The earliest that the roll discrimination algorithm could beginto deploy the airbags would then be about 60 milliseconds after thestart of the roll event (entrance time plus 40 milliseconds). Thefastest observed head closure times are on the order of 115 millisecondsafter the start of the roll event. Given that the associated dataprocessing and safety restraint deployment (e.g. airbag inflation) takesabout 30 milliseconds, the safety restraint actuator 30 would be fullydeployed for these cases at about 90 milliseconds after the start of theroll event. The minimum fire time Δt^(min) ensures that the informationprovided in the signals from lateral accelerometer 18 and angular ratesensor 20 has been utilized as much as possible while still enabling adeployment decision to be made in time to avoid head closure for severeevents. The maximum firing time Δt^(max) reduces the vulnerability ofthe roll discrimination algorithm to concatenated events, and may alsoenable the roll discrimination algorithm to reset and catch a second“real” initiator of a rollover in an accident where the second of twotime-separated lateral events leads to rollover. If, in step (330.1),the measures event time Δt^(M) is within the specified range, then thefirst detection condition is met, and additional detection criteria areevaluated in step (330.1). Otherwise, the process continues with step(150) for the next iteration.

[0114] As a second detection condition of step (330.1), thefigure-of-merit FOM is compared with a threshold function FOM^(Thr)(Δt^(M)) that, for the exemplary vehicle platform, provides forsufficiently fast discrimination times for substantially all events asnecessary in accordance with the above-described detection philosophy.The threshold function FOM^(Thr)(Δt^(M)), for example, has the followingform:

FOM ^(Thr)(Δt ^(M))=A·Δt ^(M) +B

[0115] The associated second detection condition is given by:

FOM(n ^(M))>FOM ^(Thr)(Δt ^(M))

[0116] For example, based upon data from a set of rollover tests of aparticular type of vehicle, A and B were given as A=6.46*10¹¹(g²deg⁶/ms*s⁴) and B=−2.34*10¹³ (g²deg⁶/s⁴) for (40milliseconds≦Δt^(M)<96 milliseconds), and as A=2.59*10¹¹ (g²deg⁶/ms*s⁴)and B−1.36*10¹³ (g²deg⁶/s⁴) for (96 milliseconds≦Δt^(M)≦165milliseconds). The figure-of-merit FOM and the threshold functionFOM^(Thr)(Δt^(M)), for example, both have engineering units of[g²deg⁶/s⁴]. Generally, different types of vehicles would have eitherdifferent parameter values or different functional forms for thethreshold function FOM^(Thr)(Δt^(M)). A multi-segmented thresholdfunction FOM^(Thr)(Δt^(M)), e.g. comprising a plurality of linearsegments, has been found to be beneficial to the performance of the rolldiscrimination algorithm. The above exemplary threshold line wasdeveloped from data that was sampled at a rate of 1250 Hz for a timestep of 0.8 milliseconds. The threshold function FOM^(Thr)(Δt^(M)) wouldbe different for different data sampling rates because of differences inthe resultants of integrations involved in calculating thefigure-of-merit FOM. Generally, the threshold function FOM^(Thr)(Δt^(M))could be represented by either a function of time, a piecewise functionof time, or a table lookup with respect to time. Furthermore, whereasthe threshold function FOM^(Thr)(Δt^(M)) is generally a function oftime—e.g. time period since inception—, it should be understood thatthis threshold function FOM^(Thr)(Δt^(M)) could in some cases beconstant, i.e. constant with respect to time. If, in step (330.1), thefigure-of-merit FOM exceeds the threshold function FOM^(Thr)(Δt^(M)),then the second detection condition is met, and additional detectioncriteria are evaluated in step (330.1). Otherwise, the process continueswith step (150) for the next iteration.

[0117] As a third detection condition of step (330.1), thefigure-of-merit FOM is tested to see if it is increasing in magnitudewith respect to time at the time of prospective deployment of the safetyrestraint actuator(s) 30, as follows:

|FOM(n ^(M))|>|FOM(n ^(M)−1)|AND

|FOM(n ^(M))|>|FOM(n ^(M) −m)|, where m>1, e.g. m=6

[0118] The third detection condition is intended to prevent deploymentin cases, for example, for which the threshold function FOM^(Thr)(Δt) isexceeded, e.g. at Δt=40 milliseconds, but for which the event wasdecaying away (e.g. for which the magnitude of either A_(y) or ω_(x) orboth was decreasing). If, in step (330.1), the figure-of-merit FOM isincreasing with respect to time, then the third detection condition ismet and additional detection criteria are evaluated in step (330.1).Otherwise, the process continues with step (150) for the next iteration.

[0119] As a fourth detection condition of step (330.1), the magnitude ofthe compensated lateral acceleration component A′_(y) at the time ofprospective deployment of the safety restraint actuator(s) 30) iscompared with a second acceleration threshold A_(y)^(Thr_2),

[0120] , as follows: A_(y)^(′)(n^(M)) > A_(y)^(Thr_2)

[0121] The fourth detection condition prevents a failure of the angularrate sensor 20 in a mode that causes a large, false compensated angularvelocity ω′_(x) signal from causing an inadvertent deployment of thesafety restraint actuator(s) 30. For example, a second accelerationthreshold A_(y)^(Thr_2)

[0122] value of 0.7 g would likely not be exceeded during normal drivingconditions for which there is no lateral tire slip on the drivingsurface. If, in step (330.1), the magnitude compensated lateralacceleration component A′_(y) greater than the second accelerationthreshold A_(y)^(Thr_2),

[0123] , then the fourth detection condition is met and additionaldetection criteria are evaluated in step (330.1). Otherwise, the processcontinues with step (150) for the next iteration.

[0124] As a fifth detection condition of step (330.1), the magnitude ofthe compensated angular velocity ω′_(x) is compared with an associatedsecond roll rate threshold ω^(Thr) ^(_(—)) ² at the time of prospectivedeployment of the safety restraint actuator(s) 30, as follows:ω_(x)^(′)(n^(M)) > ω^(Thr_2)

[0125] For example, the second roll rate threshold ω^(Thr) ^(_(—)) ² isabout 50 degrees/second. The fifth detection condition ensures that thevehicle 12 is experiencing significant angular velocity at the time ofdeployment of the safety restraint actuator(s) 30. The second and fifthdetection conditions in combination prevent severe side impact eventsfrom deploying the safety restraint actuator(s) 30. The fifth detectioncondition also prevents a failed lateral accelerometer 18—indicating alarge, false lateral acceleration signal—from causing an inadvertentdeployment of the safety restraint actuator(s) 30. If, in step (330.1),the magnitude of the compensated angular velocity ω′_(x) greater thanthe second roll rate threshold ω^(Thr) ^(_(—)) ² then the fifthdetection condition is met, and the process continues with step (340).Otherwise, the process continues with step (150) for the next iteration.

[0126] The herein-described measures algorithm 300.1 has beensuccessfully tested with data from a series of vehicle rollover tests,and has been demonstrated to provide a reliable prediction of eventualvehicle rollover. For roll events caused by high lateral acceleration,predictions can be made relatively quickly, which enables the measuresalgorithm 300.1 to deploy the airbags before head closure for the typeof roll events where head closure typically occurs most rapidly.Generally, the measures algorithm 300.1 is beneficial in providingrelatively early rollover detection and relatively early time-to-fire(TTF's) of the associated safety restraint actuator(s) 30, for short andmedium time roll events, similar to curb trip and high-g lateraldeceleration type events.

[0127] Accordingly, the rollover detection system 10 incorporating themeasures algorithm 300.1 provides for improved discrimination of vehiclerollover that allows for rollover airbag deployment times that meetoccupant head closure times while minimizing inadvertent deployments,by:

[0128] utilizing the measured lateral acceleration to aid in predictingfuture (20-30 ms later) roll motion;

[0129] combining lateral acceleration with angular speed and totalrotation angle to produce a measure of the current rotation state anddynamics, and the forcing function that is producing the rotation,without requiring the use of initial vehicle angle information for rollevents where the starting angle is less than about 20 degrees fromhorizontal; and

[0130] utilizing vehicle-specific dynamics properties (as derived fromrollover test data) combined with early measured vehicle responses toallow for a prediction of eventual vehicle rollover before such outcomeis definitive.

[0131] Referring to FIGS. 10 four different vehicle testconditions—designated as Test A, Test B, Test C and Test D, aretabulated for purposes of illustrating and comparing the measuresalgorithm 300.1 and the energy algorithm 300.2 (the energy algorithm300.2 is described more fully hereinbelow). Tests A and B are corkscrewtype tests, which illustrate conditions for which the energy algorithm300.2 exhibits faster rollover detection than the measures algorithm300.1, and Tests C and D are deceleration sled tests for which themeasures algorithm 300.1 exhibits faster rollover detection than theenergy algorithm 300.2. The vehicle rolled over in Tests A and D, butdid not roll over in Tests B and C, but rather achieved a maximum rollangle of 37 and 34 degrees respectively. The initial vehicle speed,average vehicle deceleration, and associated detection and event timesare also tabulated in FIG. 10, wherein the head closure time is the timeat which the head of the occupant (dummy) actual struck the interior ofthe vehicle.

[0132] Referring to FIGS. 11a-d, the filtered roll rate (angular rate)from an angular rate sensor 20, roll angle, and filtered lateralacceleration from a lateral accelerometer 18 are illustrated as afunction of time for each of Tests A-D respectively in accordance withthe conditions that are tabulated in FIG. 10.

[0133] Referring to FIG. 12, the calculated figure-of-merit FOM isplotted for Tests C and D as a function of measures event time Δt^(M),i.e. the time since inception of the measures algorithm 300.1 for actualsled deceleration tests of a particular type of vehicle in accordancewith the table of FIG. 10. FIG. 12 also illustrates an associatedthreshold function FOM^(Thr)(Δt^(M)) for the particular type of vehicle.Test D caused the vehicle to rollover and Test C reached a maximumrotation angle of about 34 degrees. The figure-of-merit FOM(n^(M))calculated by the herein-described measures algorithm 300.1 inconjunction with the associated threshold function FOM^(Thr)(Δt^(M)),enabled a firing time (TTF) of 98 milliseconds after inception of theroll event for test D, for which the vehicle rolled over, which wassubstantially before the associated head closure time of 196milliseconds, thereby providing 98 milliseconds within which to deploythe associated one or more safety restraint actuators 30. The safingcriteria of associated safing algorithm 200 were satisfied 26milliseconds after inception of the roll event, which was substantiallybefore the detection criteria was satisfied by the measures algorithm300.1. By comparison, the detection criteria of the hereinbelowdescribed energy algorithm 300.2 were not satisfied for the event ofTest D until 594 milliseconds after inception of the roll event, whichwas substantially after the associated head closure time, therebyillustrating the benefit of the measures algorithm 300.1 for the rollevent of Test D.

[0134] Referring to FIG. 6, FIGS. 8a-c, and FIGS. 9a-b, the energyalgorithm 300.2 will now be discussed with greater particularity,wherein the steps of FIG. 6 are suffixed with “0.2” to indicate theirassociation therewith. The ONGOING_EVENT_FLAG for energy algorithm300.2—referred to as the ONGOING_ENERGY_EVENT_FLAG—is set in step(308.2) upon satisfaction of the entrance criteria in step (306.2), andis reset in step (320.2) upon satisfaction of the exit criteria in step(322.2). The ONGOING_ENERGY_EVENT_FLAG, for example, could correspond toa particular location in the memory 28 of the associated processor 26that implements the energy algorithm 300.2. After entry following step(306.2), the energy algorithm 300.2 is not subsequently exited untileither the energy event exit criteria is satisfied in step (322.2), oruntil a roll event is detected causing a deployment of the safetyrestraint actuators 30. Moreover, after the energy event exit criteriais satisfied and the energy algorithm 300.2 is exited, the energyalgorithm 300.2 can be subsequently reentered if the associated energyevent entrance criteria is subsequently satisfied.

[0135] The energy algorithm 300.2 utilizes the angular velocity saxsignal from angular rate sensor 20 to determine the roll state of thevehicle and compare the total energy (rotational kinetic and potential)of the vehicle 12 with that needed to completely roll.

[0136] In step (306.2), the entrance criteria of the energy algorithm300.2 is, for example, that the magnitude of the compensated lateralacceleration components A′_(y) be greater than a first accelerationthreshold A_(y)^(Thr_1),

[0137] , OR that the magnitude of the compensated angular velocityω′_(x) be greater than a first roll rate threshold ω^(Thr) ^(_(—)) ¹i.e.:A_(y)^(′)(n^(E)) > A_(y)^(Thr_1)  OR  ω_(x)^(′)(n^(E)) > ω^(Thr_1)

[0138] For an example of a particular type of vehicle, based upon actualrollover data, the first acceleration threshold A_(y)^(Thr_1)

[0139] was set to about 1.4 g (as for the measures algorithm 300.1) andthe first roll rate threshold ω^(Thr) ^(_(—)) ¹ was set to about 19degrees/second. It should be recognized that this threshold value, aswell as the value of the other parameters of the energy algorithm 300.2,is generally dependent upon the characteristics of the particularassociated vehicle 12 or class of vehicles, and that the particularvalue used for a particular rollover detection system 10 can be adjustedfor improved discrimination dependent upon the nature of the associatedvehicle 12 or class of vehicles.

[0140] In step (310.2), upon initial entrance to the energy algorithm300.2 following step (306.1), the energy algorithm 300.2 is initialized.An event sample count n^(E) and the value of angular position θ^(E)(−1)are initialized—e.g. to values of zero. Also the sampled time t^(E)(−1)just prior to the time of event entrance is initialized to a value ofthe time of energy event entrance t^(E)(0), which is initialized to avalue of the current time t; and the time period Δt^(E)(0) sincealgorithm entrance is initialized to a value of zero. Furthermore, asecond event sample count n^(ω) ^(E) is initialized to zero, as is atime period Δt^(E)* since roll direction change. The superscript “E”used herein refers to variables associated with the energy algorithm300.2.

[0141] Upon subsequent iteration of the energy algorithm 300.2, if, instep (304.2), the ONGOING_ENERGY_EVENT_FLAG is set, then, in step(312.2), the event sample count n^(E) is incremented, the associatedcurrent sampled time t^(E)(n^(E)) is set equal to the current time t,and the energy event time Δt^(E) is calculated as the period extendingfrom the time of energy event entrance t^(E)(0) to the current timet^(E)(n^(E)) as follows:

Δt ^(E)(n ^(E))=t ^(E)(n ^(E))−t ^(E)(0)

[0142] In step (322.2), one exit criteria of the energy algorithm 300.2is, for example, that the energy event time Δt^(E) be greater than amaximum time period threshold Δ  t_(max)^(E),

[0143] , i.e.: Δ  t^(E)(n^(E)) > Δ  t_(max)^(E)

[0144] Another exit criteria of the energy algorithm 300.2 is, forexample, that the energy event time Δt^(E) be greater than a minimumtime period threshold Δ  t_(min)^(E),

[0145] , and that the time period since the entrance criteria of step(306.2) was most recently satisfied is greater than a second time periodthreshold Δ  t_(Event)^(E),

[0146] , i.e., as follows:Δ  t^(E)(n^(E)) > Δ  t_(min)^(E)  AND  Δ  t^(E)(n^(E)) − Δ  t^(E*) > Δ  t_(Event)^(E)

[0147] The energy algorithm 300.2 requires a substantially longer periodof time than the measures algorithm 300.1 before being restarted (i.e.exited and reset) because of possibility of relatively slow rolloverevents. For the example of a particular type of vehicle, based uponactual rollover data, the time period threshold Δ  t_(max)^(E)

[0148] was set to about 12 seconds, the minimum time period thresholdΔ  t_(min)^(E)

[0149] was set to about 4 seconds, and the second time period thresholdΔ  t_(Event)^(E)

[0150] was set to about 2 seconds. Accordingly, for this example, theenergy algorithm 300.2 is executed for at least 4 seconds but not morethan 12 seconds, and subject to these limitations, is exited if the timeperiod since the entrance criteria was most recently satisfied exceeds 2seconds. Upon exit from the energy algorithm 300.2, theONGOING_ENERGY_EVENT_FLAG is reset in step (320.2), after which asubsequent satisfaction of the entrance criteria in step (306.2) causesthe variables associated with the energy algorithm 300.2 to beinitialized in step (310.2).

[0151] If, in step (322.2), the exit criteria is not satisfied, then thealgorithm calculations are updated in step (326.2) for the particulariteration of the energy algorithm 300.2, as follows.

[0152] First the angular position θ^(E) is estimated by integrating thesigned value of the compensated angular velocity ω′_(x) as follows:

θ^(E)(n ^(E))=θ^(E)(n ^(E)−1)+ω′_(x)(n ^(E))·dt

[0153] wherein the integration time step dt is given by the differencebetween the time t^(E)(n^(E)) at the current iteration, and the time atthe previous iteration t^(E)(n ^(E)−1)—which difference would beconstant for a uniform sampling rate—as follows:

dt=t ^(E)(n ^(E))−t ^(E)(n ^(E)−1)

[0154] and the compensated angular velocity ω′_(x) is given by:${\omega_{x}^{\prime}(t)} = {{{\overset{\sim}{\omega}}_{x}(t)} - {{\overset{\sim}{\omega}}_{x}^{offset}(t)}}$

[0155] In step (326.2), the algorithm calculations are further adaptedto compensate for offsets in the angular velocity ω_(x) signal dueeither to gyroscope error, or to an offset as a result of significantvehicle motion, that may not otherwise be adequately compensated in thecompensated angular velocity ω′_(x), particularly for rough roadconditions for which the angular velocity ω_(x) signal may exhibitsubstantial oscillatory behavior. The energy algorithm 300.2 does notexit for at least Δ  t_(Event)^(E)

[0156] seconds, e.g. 2 seconds, following the most recent time at whichthe algorithm entrance criteria were satisfied, which thereby providesfor extending the duration of the energy algorithm 300.2 for up toΔ  t_(max)^(E)

[0157] seconds, e.g. 12 seconds, which can lead to a substantial rollangle integration errors (e.g. 24 to 36 degrees) for a relatively smalloffset—e.g. 2-3 degrees/second—in the signal from the angular ratesensor 20. On a rough road, the vehicle 12 can exhibit substantialoscillatory roll motion, and a “rough road event” would be characterizedby an angular velocity ox that oscillates about the true angularvelocity offset${{\overset{\_}{\overset{\sim}{\omega}}}_{x}^{Offset}(t)}.$

[0158] . For example, referring to FIG. 13, an angular velocity ω_(x)signal having a true angular velocity offset${\overset{\_}{\overset{\sim}{\omega}}}_{x}^{Offset}(t)$

[0159] of −6.5 degrees/second is plotted as a function of time. Becausetypical roll events do not exhibit a change in sign of compensatedangular velocity ω′_(x) during the roll event, it is possible torecognize a rough road condition from oscillation in the compensatedangular velocity ω′_(x) signal. Under these conditions, the integratedroll angle θ^(E) is damped toward zero degrees every time thecompensated angular velocity ω′_(x) changes sign, according to thefollowing equation:${\theta^{E}\left( n^{E} \right)} = {{{\theta^{E}\left( {n^{E} - 1} \right)} \cdot {{MAX}\left( {\frac{1024 - \left( {n^{E} - n_{\omega}^{E}} \right)}{1024},0.5} \right)}}\quad {and}}$n_(ω)^(E) = n^(E)

[0160] wherein the counter n^(ω) ^(E) is set equal to the event samplecount n^(E) at the time of reversal, which provides for damping the rollangle θ^(E) by an amount between 0.1% and 50% each time the compensatedangular velocity ω′_(x) changes direction, depending upon the period oftime since the most recent change of direction.

[0161] Referring to FIG. 14, the affect of the above-describedcompensation for the roll oscillation effect is illustrated, wherein theroll angle θ^(E), integrated from the angular velocity ω_(x) (roll rate)data plotted in FIG. 13, is plotted as a function of time for variousconditions. As the first condition, the true angular velocity offset${\overset{\_}{\overset{\sim}{\omega}}}_{x}^{Offset}$

[0162] of −6.5 degrees/second is removed prior to integration. As thesecond condition, the roll angle θ^(E) is integrated from the biasedangular velocity ω_(x) data, and then compensated for roll oscillationas described hereinabove. As the third condition, the roll angle θ^(E)is integrated from the biased angular velocity ω_(x) data without theabove-described compensation for roll oscillation, which illustrates thepotential for false detection of a roll event as a result of anuncompensated angular velocity ω_(x) bias for relatively longintegration intervals. The above-described compensation for rolloscillation substantially corrects for roll-oscillation inducedintegration errors, without adversely affecting the detection of anactual roll event for which the angular velocity co, is substantiallyunidirectional.

[0163] In step (326.2), the algorithm calculations further provide forrecording the latest time at which the entrance criteria of step (306.2)are satisfied, so as to provide a supplemental basis for the exitcriteria of step (322.2), as follows:If  A_(y)^(′)(n^(E)) > A_(y)^(Thr_1)  OR  ω_(x)^(′)(n^(E)) > ω_(x)^(Thr_1)  then  Δ  t^(E^(*)) = Δ  t^(E)

[0164] Following the algorithm calculations of step (322.2), thealgorithm detection criteria evaluated in step (330.2) comprise aplurality of detection conditions, for example, as illustrated in FIG.8c. If all of the detection conditions are satisfied—so that generallyan energy event threshold is exceeded—then a rollover is consideredlikely to occur, and if in step (340), an associated safing criteria issatisfied from the safing algorithm 200, then in step (350), theassociated one or more safety restraint actuators 30 are deployed so asto mitigate injury to the associated occupant or occupants. Thedetection criteria of the energy algorithm 300.2 are established inaccordance with a detection philosophy similar to that describedhereinabove for the measures algorithm 300.1.

[0165] The principal detection criteria of the energy algorithm 300.2are based upon the behavior of the compensated angular velocity ω′_(x)and roll angle θ^(E), and the associated trajectory thereof, in theassociated phase-space of angular velocity and roll angle (i.e. the ω-θphase-space). An example of the ω-θ phase-space is illustrated in FIG.15.

[0166] In accordance with rigid body dynamics, there exists atheoretical threshold boundary in phase-space that distinguishes betweenroll and non-roll events of an associated rigid body. For example, thistheoretical threshold boundary is given by:${\omega^{Thr}(\theta)} = \sqrt{\frac{2m\quad {g \cdot \left\lbrack {\frac{T^{2}}{4} + h_{CG}^{2}} \right\rbrack^{\frac{1}{2}} \cdot \left\lbrack {1 - {\sin \left( {\theta + {\tan^{- 1}\left( \frac{2h_{CG}}{T} \right)}} \right)}} \right\rbrack}}{I}}$

[0167] where mg is the weight of the vehicle, T is the vehicle trackwidth, I is the vehicle moment of inertia in roll, and h_(CG) is theheight of the vehicle center of gravity. This equation is nearly linearin the ω-θ plane over the region of interest. However, because ofnon-rigid body effects, the practical threshold boundary is beneficiallymodeled as a piecewise-linear boundary comprising, for example, a seriesof about 5 or 6 connected line segments that generally follow the abovetheoretical threshold boundary, but which can be tailored for aparticular vehicle 12 or vehicle platform to improve discriminationbetween roll and non-roll events. Generally, this boundary could berepresented by either a function in phase-space (e.g. a function of rollangle θ), a piecewise function in phase-space (e.g. a piecewise functionof roll angle θ), or a table lookup in phase-space. Referring to FIG.15, actual rollover test data—filtered using the hereinabove-describedrunning average filter—for Tests A and B of FIGS. 11a and 11 brespectively, in accordance with the conditions of FIG. 10, is plottedin the ω-θ phase-space, together with an example of the associatedtheoretical threshold boundary and an example of a practical,piecewise-linear threshold boundary.

[0168] The distance between the current ordered pair (ω′_(x)(n^(E)),θ^(E) (n^(E))) and the linear segment of the practical thresholdboundary is calculated for each iteration for the linear segment 10whose associated endpoint angle values θ_(k), θ_(k+1) bound the currentroll angle θ^(E)(n^(E)). Each linear segment of the practical thresholdboundary is defined by its endpoints (ω_(k),θ_(k)) and (ω_(k+1),θ_(k+1)). The distance D between the current ordered pair and theappropriate linear segment of the practical threshold boundary is givenby:${D\left( {{\overset{\sim}{\omega}}_{x},\theta^{E},n^{E},k} \right)} = \frac{\left\lbrack {{\left( {\omega_{k + 1} - \omega_{k}} \right) \cdot \left( {{\theta^{E}\left( n^{E} \right)} - \theta_{k}} \right)} - {\left( {\theta_{k + 1} - \theta_{k}} \right) \cdot \left( {{{\omega_{x}^{\prime}\left( n^{E} \right)}} - \omega_{k}} \right)}} \right\rbrack}{\sqrt{\left( {\theta_{k + 1} - \theta_{k}} \right)^{2} + \left( {\omega_{k + 1} - \omega_{k}} \right)^{2}}}$

[0169] whereby, if this distance is less than zero, then the practicalthreshold boundary has been crossed.

[0170] The slope of the trajectory of (ω′_(x)(n^(E)), θ^(E)(n^(E))) inthe ω-θ phase-space is given by:${{Slope}\left( n^{E} \right)} = \frac{{\omega_{x}^{\prime}\left( n^{E} \right)} - {\omega_{x}^{\prime}\left( {n^{E} - 1} \right)}}{{\theta^{E}\left( n^{E} \right)} - {\theta^{E}\left( {n^{E} - 1} \right)}}$

[0171] and the associated angle of this slope in the ω-θ phase-space isgiven by:$\beta = {\tan^{- 1}\left( {{{Slope}\left( n^{E} \right)} \cdot \frac{180}{\pi}} \right)}$

[0172] If, in step (330.2), the angle β is within limits (i.e.β^(min)<β<β^(max), where e.g. β^(min)=75 degrees and β^(max)=90degrees), the magnitude of the roll rate is increasing with time (i.e.|ω′_(x)(n^(E))|−|ω′_(x)(n^(E)−1)|>0), the distance to the practicalthreshold boundary is less than zero (i.e. D({tilde over (ω)}′_(x),θ^(E), n^(E), k)<0) and the roll angle θ^(E) is greater than a rollangle threshold θ^(Thr) (i.e. |θ^(E)>θ^(Thr), where e.g. θ^(Thr)=10degrees), then the energy detection criteria are satisfied. Alternately,the energy detection criteria are satisfied if the distance in ω-θphase-space is less than a threshold D^(Thr) (i.e. D({tilde over(ω)}′_(x), θ^(E), b^(E), k)<D^(Thr), where e.g. D^(Thr)=−2.5{squareroot}{square root over (deg²+(deg/sec)²)}) and the roll angle θ^(E) isgreater than the roll angle threshold θ^(Thr) (i.e. |θ^(E)|>θ^(Thr)). Ifthe energy detection criteria are satisfied in step (330.2), and if, instep (340), the safing criteria are satisfied, then, in step (350), theassociated one or more safety restraint actuators 30 are deployed so asto mitigate injury to the associated occupant or occupants.

[0173] The energy algorithm 300.2 deployment decision is not latched, sothat, if the safing criteria has not been satisfied by the time thedetection criteria of the energy algorithm 300.2 is satisfied, then theenergy algorithm 300.2 continues to be iterated until either the safingcriteria is satisfied, or the energy algorithm 300.2 is otherwise exitedin step (322.2)

[0174] It should be understood that the measures algorithm 300.1 and theenergy algorithm 300.2 can be executed in series or in parallel, on acommon processor 26 or on separate processors 26. If executed in series,then the steps illustrated in FIG. 6 for one iteration are completed forone of the algorithms, then the other algorithm would commence witheither step (302) for the first pass, or step (150) for subsequentpasses.

[0175] Whereas the rollover detection algorithm has been illustratedwith equations in a particular form, it should be understood that thesecalculations may be implemented on a particular processor 26 in avariety of ways without departing from the scope of the teachingsherein. For example, the particular calculations described herein mayrequire modification in order to be practically implemented on aparticular processor, for example, depending upon the resolution ofassociated analog-to-digital converters, and the type and precision ofmathematical operations that can be performed by the particularprocessor 26, and the preferred word size of the particular processor26.

[0176] Whereas the roll discrimination algorithm is illustrated hereinas applied to sampled data, it should be understood that the algorithmcould also be implemented continuously, for example, using an analogprocessor. Moreover, it should be understood that the event sample countn^(M) may be either explicit or implicit in the actual implementation ofthe roll discrimination algorithm, and that the associatedtime-dependent variables can be expressed as functions of either time tor event sample count n^(M), n^(E).

[0177] Whereas the measures algorithm 300.1 and the energy algorithm300.2 have been illustrated as utilizing a measure of roll angle that isfound by integrating the associated compensated angular velocity ω′_(x),it should be understood that a measured roll angle, e.g. from an inclinesensor, could be used instead of a calculated roll angle.

[0178] Referring to FIG. 16, in accordance with another embodiment, arollover detection system 10.1 comprises the rollover detection system10 as illustrated in FIG. 2 and described hereinabove, and furthercomprises a lateral velocity sensor 42 that is operatively connected tothe processor 26, and which is adapted to provide a measure of thelateral velocity of the vehicle 12 with respect to the ground surface,e.g. a road surface. The lateral velocity sensor 42 could be based uponany of various sensing technologies, including but not limited to waveor pulse based transmit and receive system based upon sound (orultrasound), microwave, laser, radar, or other electromagnetictechnology, e.g. by measuring speed responsive to a Doppler shift of anassociated carrier wave; or an optical velocity sensor that relies uponthe underlying spatial frequencies in an image of the ground surface.The lateral velocity sensor 42, for example, would be mounted on adownward or sideways facing surface of the vehicle, such as theundercarriage, under side of a side mirror, or lower vehicle body panel,for example, with the transmitter directed downward at the road surfacesuch that the primary axis of the transmitted signal would be at someangle other than 0 degrees with respect to the vertical as viewed fromthe rear or the vehicle, for example, with the transmitter laterallytilted at about 45 degrees for a useful compromise between signalstrength and sensor sensitivity. The receiver, for example, would belocated some lateral distance away from the transmitter so as to receivea wave emitted from the transmitter and reflected from the road surface,for a normal vehicle driving height. Alternately, the transmitter couldbe oriented substantially parallel to the ground so as to measure thevelocity relative to reflective surfaces proximate to and elevated fromthe road surface. The receiver could be located near the transmitter forease in mounting, but possibly at the expense of a reduction in signalstrength.

[0179] The measure of lateral velocity from the lateral velocity sensor42 can be used to improve the discrimination of roll events by therollover detection system 10.1. Many roll events—particularly trippedroll events—exhibit pre-roll motion that includes significant lateralvehicle velocity. As the vehicle 12 experiences lateral decelerationforces from the tires sliding laterally and possibly engaging someobstacle or ground feature, the lateral deceleration forces create thetorque on the vehicle 12 about the longitudinal axis causing the vehicle12 to roll, whereby the initial lateral translational kinetic energyassociated with the initial lateral velocity is converted to rotationalkinetic energy and potential energy. In accordance with the conservationof energy, absent other roll inducing forces—e.g. vertical forces thatmight convert the longitudinal translational kinetic energy associatedwith the vehicle's forward velocity to rotational kinetic energy—thevehicle would not likely roll over responsive to a conversion of thelateral kinetic energy unless the lateral kinetic energy$\left( {\frac{1}{2}{mass}_{veh}*v^{2}} \right)$

[0180] is greater than the potential energy (mass_(veh)*g*Δh) associatedwith raising the vehicle center of gravity to the equilibrium height Δhassociated with the vehicle on two same-side wheels. Accordingly, ameasure of vehicle lateral velocity or speed can provide an earlyindication of whether or not the vehicle has sufficient energy to rollover. If the vehicle lateral velocity is insufficient to cause acomplete rollover (i.e. if V≦{square root}{square root over (2gΔh)}),then the deployment of associated safety restraint actuators 30 can bedelayed or inhibited, even for the most initially severe partial rollevents.

[0181] For example, a vehicle 12 sliding laterally into a fixed curbwith lateral impact velocity of 10 mph may likely not roll over, butinstead, would be subject to a relatively large, but short-lived,lateral acceleration and roll rate lasting on the order of ½ second.However, a similar curb impact event with an initial lateral speed of atleast 15 mph would likely result in a vehicle rollover with anassociated occupant head closure time of about 100 to 150 ms afterinitial impact. A rollover decision criteria adapted to deploy thesafety restraint actuators 30 prior to occupant head closure for thelatter rollover event, would likely result in deployment of the safetyrestraint actuators 30 responsive to the former non-roll event if therollover decision criteria were not otherwise responsive to vehiclelateral speed. If the vehicle lateral speed is known, then thedeployment of all or some rollover restraints can be inhibited at anotherwise relatively early decision time that would be necessary tootherwise deploy the safety restraint actuators 30 prior to occupanthead closure. The roll motion could continue to be monitored by therollover detection system 10.1, and safety restraint actuators 30 couldbe deployed at later times if the conditions changed to those that wouldlead to a complete rollover.

[0182] In accordance with another embodiment of the rollover detectionsystem 10.1, the associated measures algorithm 300.1 or the energyalgorithm 300.2 could incorporate two or more different deploymentthresholds, the selection of which would be dependent upon the lateralspeed of the vehicle at or near the rollover algorithm entrance. Thethreshold could be a function of initial lateral velocity such that forlower initial lateral velocities, correspondingly larger thresholds forone or more rollover measures would be required to be exceeded in orderfor the associated safety restraint actuators 30 to be deployed.

[0183] The initial lateral velocity of the vehicle 12 does notnecessarily account for all of the translational kinetic energyavailable to be transformed into rotational kinetic energy that wouldpossibly lead to rollover. For example, a vehicle that is travelingforward has a longitudinal translational energy that can be convertedinto lateral kinetic energy, for example, if the vehicle 12 undergoes aspin on a slippery surface. If this vehicle simultaneously undergoesroll motion, then as the roll proceeds, the rotational kinetic energyand the rotation induced potential energy may increase withoutsignificantly depleting the kinetic energy associated with the initiallateral velocity of the vehicle 12.

[0184] In accordance with another embodiment, if the total translationalkinetic energy—i.e. lateral plus longitudinal—is less than a thresholdcorresponding to the rotational potential energy at the roll equilibriumposition of the vehicle 12, then the deployment of the associated safetyrestraint actuators 30 could be inhibited because there would beinsufficient energy to cause the vehicle to completely roll over.

[0185] In accordance with another embodiment of the rollover detectionsystem 10.1, the lateral velocity of the vehicle 12 is monitored duringthe initial stages of the event to determine if the current lateralkinetic energy plus rotational kinetic energy plus potential energyexceeds the energy required for vehicle rollover. Generally, the lateralvelocity of the vehicle can be blended into the rollover algorithm todevelop a new measure—or to enhance an existing measure—of rolllikelihood, for example, that is a function of the sensed lateral speedin combination with one or more of the following vehicle dynamicsignals: longitudinal roll rate, roll tilt angle, height above the roadsurface, lateral acceleration, vertical acceleration, steering wheelangle, vehicle forward speed, or yaw rate. Combining vehicle lateralvelocity with any of these sensed vehicle state parameters can provide ameasure that enhances the ability of a rollover algorithm to morequickly estimate or predict whether or not the vehicle will rollover.

[0186] For example, in accordance with an energy-based approach, atheoretical deployment threshold in the phase space of roll rate androll angle could be of the form:

[0187] function(v_(lateral))+function(rollrate), for example:${{C_{1}*v_{lateral}^{2}} + \left( {\omega_{roll}^{2} + {\sum\limits_{time}\quad \omega_{roll}}} \right)} = C_{2}$

[0188] where C₁ is a vehicle-specific constant, v_(lateral) is thelateral speed of the vehicle, ω_(roll) is the roll rate of the vehicle,and C₂ is the potential energy required for rollover, which provides ameasure roughly proportional to the total energy that may be availableor is contributing to roll motion, i.e. the total of the lateral kineticenergy, the roll rotational kinetic energy, and theroll-angle-contributed potential energy. For purposes of comparison, thetheoretical deployment threshold illustrated in FIG. 15 is given by thelatter term of the above function, i.e.$\left( {\omega_{roll}^{2} + {\sum\limits_{time}\quad \omega_{roll}}} \right).$

[0189] . Accordingly, the former term of the above function, i.e.C₁ * v_(lateral)²

[0190] can be interpreted as a threshold-lowering offset that isdependent upon lateral velocity. Specific threshold characteristics fora particular vehicle can be tailored using either test data or analysisto relate the particular threshold function to a minimum value thatresults in vehicle rollover.

[0191] In other embodiments, the measure of lateral velocity can be usedto modify the deployment threshold function(s) of either the hereinabovedescribed energy algorithm 300.2 or the hereinabove described measuresalgorithm 300.1.

[0192] For example, referring to FIG. 17, the roll rate—roll angledeployment threshold of the energy algorithm 300.2 can be adjusted lowerresponsive to the measure of lateral velocity, as indicated by thedashed line in FIG. 17. For example, the entire threshold curve might beshifted downward by a roll rate that is dependent upon the measure oflateral velocity, in accordance with the associated lateraltranslational kinetic energy that is available to be converted into rollmotion.

[0193] As another example, referring to FIG. 18, a threshold for arollover measure that increases in magnitude for increasing rollprobability—e.g. the threshold function of the measures algorithm300.1—can be adjusted by a multiplicative factor that is a function ofthe magnitude of lateral velocity. For example, a velocity magnitude,V₁, could be chosen for which the nominal rollover deployment thresholdis not modified (threshold multiplier of 1). For lower speeds thethreshold is raised by a threshold multiplier factor (greater than 1),and for higher speeds the threshold is lowered by a threshold multiplierfactor (between 1 and 0), wherein the multiplier factor is a function ofthe measure of lateral speed. Alternately, instead of modifying thethreshold in this manner, the particular rollover measure could bechanged by adding an appropriate function of lateral velocity so as toachieve an equivalent result.

[0194] The measure of vehicle lateral velocity can be either directlymeasured—as described hereinabove—or indirectly estimated. Theestimation of lateral velocity can be based upon measurements fromsensors that would already be incorporated in the vehicle, e.g. forvehicle stability or non-roll crash sensing, thereby precluding the needfor a lateral velocity sensor to provide a direct measure of lateralvelocity.

[0195] For example, a measure of lateral velocity can be estimated usinga measurement of lateral acceleration from a lateral accelerometer,together with either a measurement of yaw rate from a yaw rate sensor,or a measurement of vehicle forward speed and steering wheel anglerespectively from a respective vehicle speed sensor and a steering wheelangle or front wheel angle sensor. The acceleration measurement from thelateral accelerometer can be integrated as a function of time to obtaina measure of lateral speed, and the output of the yaw rate sensor (orforward velocity sensor) combined with the steering wheel or front wheelangle sensor can be used to correct the integrated lateral speedresponsive to measured yaw rotational motion. For example, the lateralspeed can be estimated by integrating (or discretely summing) themeasured lateral acceleration with respect to time after subtracting thecentripetal acceleration derived from combining the yaw rate sensor (orforward velocity sensor) and the steering angle sensor as follows:v_(lateral) = ∫(A_(lateral) − ω_(yaw)² * R)t orv_(lateral) = ∫(A_(lateral) − v_(forward)²/R)t

[0196] where v_(lateral) is the calculated lateral speed of the vehicle;ω_(yaw) is the measured yaw rate of the vehicle; R is the vehicle turnradius as derived from the steering wheel angle, front tire anglesensor, or separate measures of wheel speed from separate front wheelspeed sensors; and v_(forward) is the forward vehicle speed.

[0197] The input signals used in this calculation would be low passfiltered and compensated to remove offsets. A particular type of vehiclewill have an associated maximum yaw rate, or forward velocity, that canoccur for a given steering radius, whereby a higher forward velocity oryaw rate would result in lateral tire slippage and an associated lateralvehicle speed, for typical road/tire conditions. The centripetalacceleration correction based upon either the yaw rate and vehicle turnradius or the forward speed and the vehicle turn radius would be limitedto a maximum vehicle-specific magnitude. For most vehicles with goodtires on dry pavement (ideal conditions) the correction term,ω_(yaw)² * R  or  v_(forward)²/R,

[0198] , would be limited to about ±0.8 g corresponding to thevehicle-specific maximum sustainable centripetal acceleration on typicaldry, flat pavement. In real driving situations it may be possible toachieve higher centripetal accelerations, for example, if the drivingterrain allowed the tires to dig into the driving surface.Notwithstanding that these conditions could produce a larger estimate oflateral velocity than experienced by the vehicle, these conditions arealso much more conducive to generating an actual rollover event becausethe tires and rims are potentially able to cause substantially largertorque-inducing force on the vehicle. The calculation may require somedamping term and/or conditions that allow for either only a triggeredcalculation of the lateral velocity, or an event driven reset of theestimated lateral velocity to zero, so as to preclude the adverse affectof an uncorrected offset when integrating lateral acceleration over arelatively long period of time.

[0199] The yaw rate sensor measures the rotation rate about a verticalaxis of the vehicle 12. The description hereinabove assumed that theforward vehicle velocity and yaw rate are related by a simple constant:v_(forward)=ω_(yaw)*R, which is generally true under conditions forwhich the tires do not slip on the driving surface. Under conditions forwhich the vehicle 12 tires are slipping, the vehicle 12 may have somerotational motion about a vertical axis other than the center of thecommanded turn radius, in which case the product of the yaw rate and theturn radius could be expected to exceed the forward velocity. In arollover detection system 10.1 incorporating sensors for forwardvelocity v_(forward), yaw rate ω_(yaw) and turn radius R, all three ofthese signals could be utilized to obtain both a measure of lateralvelocity and a measure of vehicle spin rate as follows: $\begin{matrix}{{v_{lateral} = {\int{\left( {A_{lateral} - {v_{forward}^{2}/R}} \right){t}}}},{{{where}\quad {v_{forward}^{2}/R}\quad {is}\quad {bounded}\quad {by}}\quad \pm A_{{centripetal}\quad {MAX}}}} \\{{{{spin}\quad {rate}} = {\omega_{yaw} - {v_{forward}/R}}},{{{where}\quad {v_{forward}/R}\quad {is}\quad {bounded}\quad {by}}\quad \pm {A_{{centripetal}\quad {MAX}}/v_{forward}}}}\end{matrix}$

[0200] Vehicle spin rate could be important because if a vehicle isprimarily spinning about a vertical axis near the mounting location ofthe lateral accelerometer, then, especially for low friction roadcondition (e.g. icy roads), the lateral accelerometer may not adequatelydetect the change in lateral velocity of the vehicle. Accordingly, thelateral velocity estimate can be further corrected as follows:v_(lateral) = ∫(A_(lateral) − v_(forward)²/R)t + v_(forward) * cos (∫spin  rate ⋅ t)

[0201] wherein the added correction term integrates the estimatedvehicle spin rate to obtain a vehicle spin angle, which is then used todetermine an estimate of the projection of the forward vehicle speedonto lateral motion that might be otherwise be undetected by the lateralaccelerometer.

[0202] The parameters of the herein-described roll discriminationalgorithm are derived from associated test data, and may requireadjustment if applied to other types of vehicles than for those forwhich the parameters were derived, wherein a criteria for the adjustmentis, for example, robust and early detection of rollover events whilealso avoiding, to the extent possible, falsely discriminatingnon-rollover events as rollover events. The particular values forvarious parameters described herein are not considered to be limiting,and, for example, may be different for different types of vehicles,which may have different susceptibilities to rollover. For example, avehicle with a relatively high center of gravity or a relatively narrowwheel-base—e.g. a sport-utility vehicle—would be more susceptible torollover than a vehicle having a relatively low center of gravity or arelatively wide wheel-base—e.g. a passenger sedan. Furthermore, therollover detection system 10 as could also be adapted to sense pitchoverevents, i.e. about the local Y-axis of the vehicle, by providing anassociated longitudinal accelerometer and a pitch rate sensor.

[0203] The lateral velocity sensor—which provides for a directmeasurement of the lateral velocity of the vehicle—and the lateralvelocity estimation algorithm described herein, provide means formeasuring or estimating lateral velocity that are substantially moreaccurate that might otherwise be inferred by either integrating only ameasure of lateral acceleration, or by using a measure of longitudinalvelocity of the vehicle, and thereby provides for improveddiscrimination of rollover events.

[0204] While specific embodiments have been described in detail, thosewith ordinary skill in the art will appreciate that variousmodifications and alternatives to those details could be developed inlight of the overall teachings of the disclosure. Accordingly, theparticular arrangements disclosed are meant to be illustrative only andnot limiting as to the scope of the invention, which is to be given thefull breadth of the appended claims, and any and all equivalentsthereof.

We claim:
 1. A system for detecting a rollover condition of a vehicle,comprising: a. a roll angular velocity sensor operatively coupled to thevehicle, wherein said roll angular velocity sensor is adapted to measurea roll rate of the vehicle about a roll axis, and said roll axis issubstantially aligned with a longitudinal axis of the vehicle; b. alateral velocity sensor operatively coupled to the vehicle, wherein saidlateral velocity sensor is responsive to a velocity of the vehicle in adirection that is substantially lateral to said vehicle, and saidlateral velocity sensor is selected from an ultrasonic sensor, amicrowave sensor, a radar sensor, and an optical velocity sensor; and c.a processor operatively coupled to said roll angular velocity sensor andto said lateral velocity sensor, wherein said processor is adapted togenerate a signal for controlling a safety restraint system, and saidsignal for controlling said safety restraint system is responsive to asignal from said roll angular velocity sensor and to a signal from saidlateral velocity sensor.
 2. A system for detecting a rollover conditionof a vehicle as recited in claims 1, wherein said processor is adaptedto determine a measure of roll angle by integrating said signal fromsaid roll angular velocity sensor, and said signal for controlling saidsafety restraint system is further responsive to said measure of rollangle.
 3. A system for detecting a rollover condition of a vehicle asrecited in claims 1, further comprising a longitudinal velocity sensoroperatively coupled to the vehicle, wherein said longitudinal velocitysensor is responsive to a velocity of the vehicle in a direction that issubstantially along said longitudinal axis of the vehicle, and saidsignal for controlling said safety restraint system is furtherresponsive to a signal from said longitudinal velocity sensor.
 4. Asystem for detecting a rollover condition of a vehicle as recited inclaims 1, further comprising an accelerometer operatively coupled to thevehicle, wherein said accelerometer is adapted to measure anacceleration of the vehicle substantially in said lateral direction,and: said signal for controlling said safety restraint system is furtherresponsive to a signal from said accelerometer.
 5. A method of providingfor detecting a rollover condition of a vehicle, comprising: a.providing for acquiring a measure of roll angular velocity of thevehicle about a roll axis, wherein said roll axis is substantiallyaligned with a longitudinal axis of the vehicle; b. providing foracquiring a measure of lateral velocity of the vehicle, wherein saidmeasure of lateral velocity is directly representative of a lateralvelocity of the vehicle; and c. providing for generating a signal forcontrolling a safety restraint system, wherein said signal forcontrolling said safety restraint system is responsive to said measureof roll angular velocity and to said measure of lateral velocity.
 6. Amethod of providing for detecting a rollover condition of a vehicle asrecited in claim 5, wherein said signal for controlling said safetyrestraint system is responsive to a deployment threshold, and saiddeployment threshold is responsive to said measure of lateral velocity.7. A method of providing for detecting a rollover condition of a vehicleas recited in claim 6, wherein said deployment threshold is shifted byan offset responsive to said measure of lateral velocity.
 8. A method ofproviding for detecting a rollover condition of a vehicle as recited inclaim 6, wherein said deployment threshold is scaled by a factorresponsive to said measure of lateral velocity.
 9. A method of providingfor detecting a rollover condition of a vehicle as recited in claim 5,further comprising: a. providing for comparing a third measure with afirst threshold, wherein said third measure is responsive to saidmeasure of lateral velocity; and b. providing for delaying or inhibitingdeployment of said safety restraint system if said third measure is lessthan said first threshold.
 10. A method of providing for detecting arollover condition of a vehicle as recited in claim 5, furthercomprising: a. providing for acquiring a measure of longitudinalvelocity of the vehicle; b. providing for determining a measure oftranslational velocity of the vehicle, wherein said measure oftranslational velocity is responsive to said measure of longitudinalvelocity and to said measure of lateral velocity; c. providing forcomparing a fourth measure with a second threshold, wherein said fourthmeasure is responsive to said measure of translational velocity; and d.providing for inhibiting deployment of said safety restraint system ifsaid fourth measure is less than said second threshold.
 11. A method ofproviding for detecting a rollover condition of a vehicle as recited inclaim 5, further comprising: a. providing for determining or acquiring ameasure of roll angle from said measure of roll angular velocity; b.providing for determining a threshold function in a phase space of saidmeasure of roll angular velocity and said measure of roll angle; c.providing for modifying said threshold function responsive to saidmeasure of lateral velocity; and d. providing for comparing a measure inphase space with said threshold function, where said measure in phasespace comprises a combination of said measure of roll angular velocityand said measure of roll angle, wherein said signal for controlling saidsafety restraint system is responsive to the operation of comparing saidmeasure in phase space with said threshold function.
 12. A method ofproviding for detecting a rollover condition of a vehicle as recited inclaim 11, wherein said threshold function comprises either a function inphase space, a piecewise function in phase space, or a table lookup inphase space.
 13. A method of providing for detecting a rollovercondition of a vehicle as recited in claim 11, wherein the operation ofmodifying said threshold function comprises determining a roll angularvelocity offset responsive to said measure of lateral velocity, andsubtracting said roll angular velocity offset from said thresholdfunction.
 14. A method of providing for detecting a rollover conditionof a vehicle as recited in claim 5, further comprising: a. generating afifth measure responsive to said measure of lateral velocity and to atleast one of a measure selected from the group comprising said measureof roll angular velocity, a measure of roll angle of the vehicle, ameasure of lateral acceleration of the vehicle, a measure of verticalacceleration of the vehicle, a measure of steering wheel angle of thevehicle, a measure of longitudinal speed of the vehicle, and a measureof yaw rate of the vehicle; b. comparing said fifth measure with a thirdthreshold; and c. controlling said safety restraint system responsive tothe operation of comparing said fifth measure with said third threshold.15. A method of providing for detecting a rollover condition of avehicle as recited in claim 14, wherein said fifth measure comprises acombination of a lateral translational kinetic energy measure and ameasure responsive to said roll rate measure, wherein said lateraltranslational kinetic energy measure is responsive to said measure oflateral velocity, and said measure responsive to said roll rate measureis responsive to at least one of a rotational kinetic energy measure anda measure of roll angle, wherein said rotational kinetic energy measureis responsive to said measure of roll angular velocity, and said measureof roll angle is responsive to an integration of said measure of angularvelocity.
 16. A method of providing for detecting a rollover conditionof a vehicle as recited in claim 5, wherein the operation of providingfor generating said signal for controlling said safety restraint systemcomprises: a. providing for acquiring a measure of lateral accelerationof the vehicle; b. providing for determining a figure of meritresponsive to said measure of lateral acceleration and said measure ofroll angular velocity; c. providing for determining a figure of meritthreshold responsive to said measure of lateral velocity; and d.providing for detecting the rollover condition by comparing said figureof merit with said figure of merit threshold.
 17. A method of providingfor detecting a rollover condition of a vehicle as recited in claim 16,wherein the operation of providing for determining a figure of meritthreshold comprises multiplying a first figure of merit threshold by athreshold multiplier, and said threshold multiplier is responsive tosaid measure of lateral velocity.
 18. A method of providing fordetecting a rollover condition of a vehicle as recited in claim 16,wherein the operation of providing for determining a figure of meritthreshold comprises adding an offset to a first figure of meritthreshold, and said offset is responsive to said measure of lateralvelocity
 19. A method of providing for detecting a rollover condition ofa vehicle, comprising: a. providing for acquiring a measure of rollangular velocity of the vehicle about a roll axis, wherein said rollaxis is substantially aligned with a longitudinal axis of the vehicle;b. providing for acquiring a measure of lateral acceleration of thevehicle; c. providing for acquiring at least one of a measure oflongitudinal velocity of the vehicle and a measure of yaw angularvelocity about a yaw axis; d. providing for determining a measure of aturn radius of the vehicle; e. providing for determining a measure oflateral velocity of the vehicle responsive to said measure of lateralacceleration, to said measure of said turn radius, and to at least oneof said measure of longitudinal velocity and said measure of yaw angularvelocity; and f. providing for generating a signal for controlling saidsafety restraint system, wherein said signal for controlling said safetyrestraint system is responsive to said measure of roll angular velocityand to said measure of lateral velocity.
 20. A method of providing fordetecting a rollover condition of a vehicle as recited in claim 19,wherein the operation of determining a measure of turn radius comprises:a. acquiring at least one of a measure of steering wheel angle, ameasure of a front tire angle, and measures of forward velocity fromseparate front wheel speed sensors; and b. determining said measure ofturn radius responsive to said at least one of a measure of steeringwheel angle, a measure of a front tire angle, and measures of forwardvelocity from separate front wheel speed sensors.
 21. A method ofproviding for detecting a rollover condition of a vehicle as recited inclaim 19, wherein the operation of providing for determining a measureof lateral velocity comprises integrating a fourth measure, wherein saidfourth measure is responsive to a difference between said measure oflateral acceleration and a measure of centripetal acceleration, and saidmeasure of centripetal acceleration is responsive to said turn radius,and to at least one of said measure of yaw angular velocity and saidmeasure of longitudinal velocity.
 22. A method of providing fordetecting a rollover condition of a vehicle as recited in claim 21,further comprising limiting a magnitude of said measure of centripetalacceleration by a centripetal acceleration threshold.
 23. A method ofproviding for detecting a rollover condition of a vehicle as recited inclaim 21, wherein said measure of centripetal acceleration comprises aproduct of said measure of yaw angular velocity and said turn radius.24. A method of providing for detecting a rollover condition of avehicle as recited in claim 21, wherein said measure of centripetalacceleration comprises said measure of longitudinal velocity divided bysaid turn radius.
 25. A method of providing for detecting a rollovercondition of a vehicle as recited in claim 21, wherein the operation ofproviding for determining a measure of lateral velocity furthercomprises: a. determining a measure of spin rate, wherein said measureof spin rate is responsive to said measure of yaw angular velocity, andto a fifth measure, wherein said fifth measure is responsive to saidmeasure of longitudinal velocity, and to said turn radius; b.integrating said measure of spin rate so as to generate a measure ofspin angle; c. generating a sixth measure by multiplying said measure oflongitudinal velocity times said spin angle; and d. generating amodified measure of lateral velocity by adding said sixth measure tosaid measure of lateral velocity.
 26. A method of providing fordetecting a rollover condition of a vehicle as recited in claim 25,further comprising limiting said fifth measure responsive to acentripetal acceleration threshold and to said measure of longitudinalvelocity.